PCA-seeded Bayesian optimisation for real-time hull response reconstruction

Mode-superposition-based conversion models enable near-real-time estimation of hull structural responses from limited measurements, yet their practical use is often hindered by subjective seed-mode selection, expensive parameter tuning, and uncertainty in measurement layout. This study presents a principal component analysis–Bayesian optimisation (PCA–BO) workflow that deterministically selects the first wave load case (WLC) mode by aligning it with the dominant PCA direction, providing a representative seed for subsequent mode selection. The remaining mode-selection variables are then tuned via data-efficient Bayesian optimisation. In addition, an RAO-similarity sensor pre-design strategy is introduced that clusters stress-RAO signatures to prioritise informative measurement locations considered. Numerical validation on an FPSO under two sea states confirms that the proposed framework improves the accuracy–efficiency trade-off. For Sea State 1, the method achieves group-aggregated Mean Absolute Error (MAE) values of 0.2741 MPa (longitudinal targets) and 0.3959 MPa (transverse targets), outperforming the conventional baseline and matching or exceeding an exhaustive grid search baseline. The offline identification cost for mode selection is reduced from 74,312 evaluations (1376.8 s) to 1500 evaluations (482.8 s). In an operational-realism test with stress-RAO perturbations, the proposed mapping is markedly less sensitive to transfer-function mismatch, yielding an approximately 80% reduction in longitudinal MAE for Sea State 2 compared with the grid-search baseline. These findings support digital-twin-oriented hull-response estimation with periodic offline updates and fast online inference, while highlighting the need for experimental calibration and sequence-aware learning to address noise, drift, and non-stationary operation.